Cut and core your pineapple into chunks. Pulse in a blender or food processor until finely diced. Reserve 1 cup of the fruit with liquid. Save the remainder for smoothies or as a topping for later.
Stir together your milk and sugar in a medium sized pot. Bring to a simmer and cook to 175 degrees or until the sugar is dissolved.
Whisk your eggs together in a small bowl. Slowly stir in a portion of your milk mixture, making sure to whisk constantly. Slowly mix the eggs back into the pot with the remaining milk and sugar.
Bring to a simmer and cook until 160 degrees or the custard coats the back of a spoon.
Remove your pan from the heat. Place in an ice bath and stir until slightly cooled.
Stir in the cream and 1 cup of your pineapple. Cover and chill 4 hours or overnight.
Freeze according to the directions of your ice cream maker.